Question

1.You are 18 today want to retire at age 65.
Starting with the day of your retirement, you would like to have an
annuity initially in the amount of $35,000 per year (but growing at
a 3% annual rate) for 35 years. You
will inherit $30,000 from your long lost uncle when you turn 34 and
save that money as part of your financial plan. Assume an interest
rate of 7% for all periods? How much must you put into your
investment account today to achieve your goal?

2You invest $12,500 in an investment that will pay you $25,000 at a
future point in time. What is the return on investment for each of
the following periods of time?

a. 4 years

b. 7 years

c. 10 years

3You want to retire at age 50; you are 20 years old today. You want to retire with a $10,000 perpetuity because you expect to live forever. In order to completely fund that perpetuity, how much do you need to save today in the bank assuming a 10% interest rate.

Answer #1

1) PV of growing annuity = P / (r - g) x [1 - ((1 + g) / (1 + r))^n]

= 35,000 / (7% - 3%) x [1 - (1.03/1.07)^35]

= $644,389.70

Its value today = FV / (1 + r)^n = 644,389.70 / (1 + 7%)^47 = $26,798.53

Value of inheritance today = 30,000 / 1.07^16 = $10,162.04

Investment required today = 26,798.53 - 10,162.04 = $16,636.50

2) Rate of return, r = (FV / PV)^(1/n) - 1

r1 = (25,000 / 12,500)^(1/4) - 1 = 18.92%

r2 = 2^(1/7) - 1 = 10.41%

r3 = 2^(1/10) - 1 = 7.18%

3) Value of perpetuity at age 50 = 10,000 / 10% = $100,000

Its value today = 100,000 / 1.1^30 = $5,731

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